Filtered backprojection is a method for image reconstruction from data, for example projection data acquired using a tomographic method. For a three-dimensional image reconstruction, two-dimensional projection data of an examined object or an object to be examined is recorded at different irradiation and/or detection angles. The projection data is then filtered and backprojected in a two-step method to obtain image data representing the original object. The Feldkamp-Davis-Kress algorithm (FDK algorithm) is a known method and is described in the publication “Practical cone-beam algorithm”, Journal of the Optical Society of America, Volume 1, No. 6, 1984 by L. A. Feldkamp et al.
The filter is a ramp filter applied on a line basis where the filtering of the projection data may be expressed mathematically as a convolution. A disadvantage is that the one-dimensional ramp filter is not local and the core has an infinitely extensive support in the position space. The disadvantage provides the presence of truncated, e.g. cut-off, projection data that does not represent the complete original object in an exact image reconstruction. Intensity changes in the edge areas of the truncated data, for example, a jump or a transition of the data values to zero, ultimately result in recognizable unwanted image artifacts, such as for example unrealistically light areas, in the reconstructed image data. The artifacts occur, for example, at the edges of the area considered for the relevant examination, that is of particular importance or interest (ROI, region of interest) and are also designated as cupping or capping artifacts.
Previous solution approaches to avoid the artifacts and to achieve as accurate a reconstruction as possible of truncated data are accompanied by increased radiation or dosage exposure of the examined object that may occur, for example, outside of the relevant area that is of interest and/or may subsequently be reconstructed.
In the publication “Wavelet localization of the Radon transform”, IEEE Transactions on Signal Processing, Volume 42, No. 8, 1994 T. Olson and J. DeStefano describe an algorithm in which the properties of wavelets are utilized to full advantage to localize largely the applied radon transformation, allowing the radiation exposure to be reduced during an examination of a limited area of an object. However, in addition to the truncated projection data at least one sparse set of untruncated projection data is required so that the radiation exposure is not limited to the ROI and a practical application may be difficult.
In the publication “Multiresolution tomographic reconstruction using wavelets”, IEEE Transactions on Image Processing, Volume 4, No. 6, 1995 A. H. Delaney and Y. Bresler describe an algorithm based on a multiscale analysis with which only a limited image area or data area is reconstructed with a high resolution. Instead of reconstructing the image data representing the originally examined object or the corresponding function from the projection data itself, a two-dimensional wavelet decomposition of the object function is constructed and the object function is determined using a conventional reconstruction or filter bank based on a multiscale analysis from the filtered coefficients of the wavelet decomposition. There is the disadvantage that an additional area of the examined object disposed around the finally reconstructed region available for a diagnosis is exposed to ionizing radiation.